Liquid dispenser systems, such as liquid soap and sanitizer dispensers, provide a user with a predetermined amount of liquid upon actuation of the dispenser. In addition, it is sometimes desirable to dispense the liquid in the form of foam by, for example, injecting air into the liquid to create a foamy mixture of liquid and air bubbles. As a general matter, it is usually preferable to reduce the space taken up by the pumping and foaming apparatus within the overall dispenser system. This maximizes the available space for storing the liquid, and has other benefits. In addition, it is desirable to have a foam pump that requires less energy to operate.